Entropy-driven Orientational Order of Topologically Modified Polymers in Confinement

Abstract

In the last few decades, there has been a sustained interest in understanding how systems at the nano-scale organize spontaneously or self-assemble to form higher-order structures. This project is an endeavor to study organizational properties in inherently disordered systems such as polymers. The key idea we propose is to control effective interactions by modulating polymer architecture (topology). We perform simulations of ring polymers that are confined in a cylindrical geometry. By introducing changes in the topology of each constituent polymer, we introduce subloops within the ring polymer. This modification of topology, combined with the confinement in the cylindrical geometry, induces entropic interactions between segments of neighboring polymers. These interactions drive the system of polymers to self-assemble into structures that maximize conformational entropy. We define certain vectors corresponding to each polymer and observe the orientational arrangement of these vectors. Finally, I also explore how one can analyze contact maps to gain a deeper understanding of polymeric systems. The principles of polymer physics presented in this thesis can be applied to study various properties of bacterial chromosomes.